PHY190 Lab Experiment 2 In-Person (Two Dimensional Motion)
PHY-190L-L3 Physics Lab 1
Fall 2020
Instructor: Dr. William Edson
Tuesday 6:00PM – 8:30PM
Email: edsonw@strose.edu
Laboratory 2 In-Person: Two Dimensional Motion
Pre-assignment
Individually complete Two Dimensional Motion prelab and turn it in over Canvas
before beginning of class.
Learning Objectives:
1.
Examine motion in two dimensions and compare horizontal and vertical
accelerations to predicted values.
2.
Linearize velocity vs. time data in two separate dimensions /to determine the
unknown accelerations.
3.
Determine an experimental value for g, the acceleration due to gravity by
interpreting the puck’s acceleration as a component of g.
In Lab Requirements:
Students will work in groups of two to complete the experimental activities
described below and will turn-in one complete set of data and results at the end of class.
Results will include plots, and answers to questions posed in the lab instructions. Be sure
to answer questions in a way that the corresponding question is easily discernable.
CAUTION:
DO NOT TOUCH THE TABLE OR SPARK GENERATOR WHEN THE
SPARKER IS ACTIVATED. TOUCH ONLY THE PLASTIC PART OF THE PUCK.
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PHY190 Lab Experiment 2 In-Person (Two Dimensional Motion)
Introduction: We will record the position of an object as it moves, and the object will
be speeding up at a constant rate (a=constant). We will again use an air table to
accomplish this. This time we will push the puck upward and to the left from the bottom
right corner of the air table so as to achieve a parabolic (curved) path of the puck.
Theory: Consider a puck moving freely on an
inclined air table (i.e. no friction) in two
dimensions.
As the puck slides along a spark occurs, this
marks the puck’s position periodically. We
therefore have a record of where the puck was
for a series of points in time
In one direction (y), gravity pulls on the puck.
The puck will be pulled downward on the air
table with a constant acceleration.
𝑔
However as the puck is moving freely and there is no friction, there is no force being
applied in the second direction (x). This means the puck will experience zero
acceleration in this direction.
We therefore have a system where constant acceleration is occurring in both planes but
only nonzero in one of them.
We would like to compile a table of data for each plane. We can measure the puck’s
displacement for each point in time in each plane. Next we can determine the puck's
velocity at several points throughout its motion.
We can find the average velocity of the puck over a time interval t.
𝑥2 − 𝑥1
⟨𝑣⟩𝑡1 →𝑡2 =
𝑡2 − 𝑡1
Note this is the average velocity NOT the instantaneous velocity.
However, for objects that experience constant acceleration (true for both planes), the
instantaneous velocity halfway between t1 and t2 is equal to the average velocity. So,
𝑥2 − 𝑥1
⟨𝑣⟩𝑡1 →𝑡2 =
= 𝑣𝑡1 +𝑡2
𝑡2 − 𝑡1
2
For example, the average velocity over the range t=.1 to t=.2 is equal to the instantaneous
velocity at t=.15s.
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PHY190 Lab Experiment 2 In-Person (Two Dimensional Motion)
Theory: Trigonometry
A
B
h
𝑝
θ
θ
θ
l
𝑎
𝑔
From A:
𝑡𝑎𝑛𝜃 =
ℎ
ℎ
→ 𝜃 = 𝑡𝑎𝑛−1 ( )
𝑙
𝑙
From B:
Due to the use of the air table, the only force which should be applying to the puck is the
gravitational force (𝐹𝑔 ) acting straight down with a total acceleration equal to the
acceleration due to gravity on Earth (𝑔). As 𝑔 is a vector, it can be broken into 2-D
components: one perpendicular to the slope plane (𝑝) and the other parallel to it (𝑎). The
angle formed between 𝑔 and 𝑝 is equivalent to the angle of the slope (θ). Therefore, if
you measure the magnitude of 𝑎:
|𝑎|
|𝑎|
𝑠𝑖𝑛𝜃 =
→ |𝑔| =
|𝑔|
𝑠𝑖𝑛𝜃
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PHY190 Lab Experiment 2 In-Person (Two Dimensional Motion)
Procedure:
1.
Level the air table. Measure the distance from the middle of the single back leg to
the line passing through the middle of both front legs of the air table (l) [see
Theory: Trigonometry section diagram A]. Measure the height of the provided
block of wood (h) and then place the block under the back leg of the table.
2. Use trigonometry to calculate the incline angle of the air track in radians.
To calculate the arctangent in Excel, use the formula ATAN(). The answer will
be given in radians.
3. Turn on the air table.
4. Turn on the spark generator and set it to 10Hz. The second puck should be at the
bottom left corner of the table throughout the experiment.
5. DO NOT TOUCH THE TABLE OR SPARK GENERATOR WHEN THE
SPARKER IS ACTIVATED. TOUCH ONLY THE PLASTIC PART OF THE
PUCK.
6. First, hold the puck near the top right corner of the spark table and simultaneously
press and hold down the spark switch and release the puck. Release the switch
prior to the puck hitting the bottom of the table. You will use this line of sparks
as your y-axis (use this to measure your displacement in x from).
7. Next, holding the puck still at the bottom right corner of the table, practice pushing
the puck upward and to the left so it follows a slow parabolic curve. You want to
ensure the puck does not hit the top or left side bars along its path.
8. When you feel you are ready, simultaneously press and hold down the spark switch
and push the puck upward and to the left.
9. The puck will travel in a parabolic path and leave a trail of dots marking its position.
10. Just before the puck hits the bottom or the left side bar, stop the sparker.
11. Mark the point where the puck was released as t = 0.
12. Using a protractor, create an x-axis which passes through your t = 0 point and is 90°
to your y-axis made using the spark table (see step 6). You will use this axis to
measure your displacement in y from.
13. Measure the puck's displacement from axes (both x and y) for the points from t=0 to
t=1.2s.
14. Calculate the magnitude of the displacements, x and Δy, for each successive set of
sparks and record your results (ex. ∆𝑥0→1 = 𝑥1 − 𝑥0 , ∆𝑥1→2 = 𝑥2 − 𝑥1 , etc.).
15. Calculate the average velocity the puck had over each .1s time interval in both the x
and y directions.
16. Plot in EXCEL the instantaneous vy vs. t in the y-direction, and instantaneous vx vs. t
in the x-direction starting with t = 0.05s. Remember that since the puck undergoes
constant acceleration, the instantaneous velocity at the middle of the time
interval is equal to the average velocity (so the instantaneous velocity at t = 0.05s
is equal to the average velocity from t = 0.00 - 0.10s).
17. On each graph make sure you have the axes labeled including units, show your best
fit line, and equation for the line indicating a value for the slope and intercept.
18. Does the behavior exhibited on each plot make sense with the theoretical
expectations? Why or why not?
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PHY190 Lab Experiment 2 In-Person (Two Dimensional Motion)
19. Using the Excel LINEST() function, determine the values and uncertainties of the
slopes from both the instantaneous vy vs. t, and instantaneous vx vs. t data.
20. Is the LINEST() result of the slope in the x-direction in agreement with the
expected value?
21. Use the LINEST() slope result from the instantaneous vy vs. t calculation to calculate
your measured value for g using trigonometry. Is your result in agreement with
the theoretical value of g (9.80 ± 0.02 m/s2)?
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